Question: Did the Old Testament sacrifices cleanse them from sin? If not, why did they have to make sacrifices?
Answer: No, the Old Testament sacrifices didn't cleanse from sin. Hebrews 10:4 says, "For it is impossible for the blood of bulls and goats to take away sins." When then, did God have people living in the Old Testament to sacrifice animals? Answer: The blood sacrifices worked like a credit card.
My wife can go to the clothing store and buy a dress by charging it to my credit card. She can wear the dress before the bill has been paid because it has been charged to my account. The credit card is a promise to pay for the dress at a future time. The Old Testament sacrifices worked like a credit card, charging their sins to Jesus' account. The people offered the sacrifices by faith, believing that at a future time the Messiah would come to pay the "sin" bill. On the Day of Atonement, the high priest sacrificed a goat for the nation of Israel. He laid his hands on another goat, which was called a scapegoat, and transferred the nations' sins to the scapegoat. When Jesus died on the cross, He paid for the sins of the world with His blood and became our scapegoat (John 1:29).